The production of magnetic maps is made difficult by background noise which systematically accompanies the measurements.
One of the difficulties consists of overcoming geomagnetic interference, particularly during periods of major magnetic activity, and possible biases of the magnetic field measurement system used. In addition, the prediction of the field is an extremely noise-sensitive operation at points located between the available measurement volume and the geological structure.
The process and apparatus according to the invention make it possible to produce very accurate maps of the magnetic field or its gradients by reducing the contribution of interference due to geomagnetic noise without having to use reference measurements for said noise (in certain particular operation modes of the invention, the accuracy is better than 1 nT and can even reach 0.1 nT, whereas in the prior art the accuracy obtained is a few nT), and the calculation of a prediction of the magnetic field or its gradients everywhere in space.
Hereinafter definitions will be given of fields of which it is wished to obtain a map and interfering fields which systematically falsify the measurements. It is also considered hereinafter that the magnetic data are obtained with field module measurement magnetometers, which at present constitute the most efficient land systems (the term "sensor" is understood to mean a probe and its associated electronics, whilst "magnetometer" is understood to mean such a sensor and a frequency meter). In the general case, other magnetometers can be used.
With the aid of this equipment and under the most general environmental conditions, the process according to the invention is of an optimum nature for obtaining readings of a geological field.
The signal measured by a magnetometer designated by its reference i and moved over the study zone or possibly fixed to the land, can be modelled with the necessary accuracy for the invention by: EQU s.sub.i (r.sub.i (t))=b.sub.geol (r.sub.i (t))+b.sub.gmag (r.sub.i (t),t)+br.sub.an (i,I.sub.i,D.sub.i,t)
In this formula, i is the index of the magnetometer (the position of the probe of the magnetometer i at a given time t is designated ri(t)) and s.sub.i is called the "earth field".
This earth field is the superimposing of all the magnetic phenemona listed hereinafter:
The magnetic sources entering the composition of the earth field can roughly be classified in accordance with their external or internal origin (cf. the document (JACOBS 89) which, like the other documents referred to hereinafter, are listed at the end of the present description).
The external part of the earth field is very weak and thus most of the earth field is due to internal sources constituting the geological field. The latter is virtually totally (approximately 99%) formed by the amplitude of the earth field.
It can itself be broken down into a Gaussian field equal to approximately 95% of the earth field, which has a deep origin, and an "anomaly" field produced by magnetized rocks of the earth's crust and the upper mantle or any magnetic source of a random nature, referred to as the local magnetic source.
The anomaly field (compared with the Gaussian field) has an amplitude of approximately 1 to 100 nT. The earth field is several dozen nanoTesla.
The external part is variable in time and constitutes the source of the geomagnetic noise (which results from a charged particle flux, which is variable as a function of time and produced by the sun). Its fluctuations have amplitudes of 1 to a few dozen nT. The noise br.sub.an is the measurement noise due to the actual measurement system.
It is mainly formed from anisotropy noise dependent on the orientation of the sensors and whose amplitude is a function of the quality of the measurement system and the sensors used. Consequently the anisotropy signal recovered by a sensor following a constant course is a constant signal.
The noise br.sub.an generally has to be taken into account for the optimum calculation of the maps and predictions.
The invention aims at determining the geological field, whose measurement is systematically disturbed by the geomagnetic noise and the anisotropy noise. Hereinafter consideration is given to the geological anomaly field.
Under the action of a magnetic field, minerals can acquire an induced magnetization directed in accordance with the exciting field (paramagnetic materials) or the opposite direction (diamagnetic materials). They can also retain a residual magnetization, due to the excitation after the latter has disappeared or has been modified (ferromagnetic materials).
Magnetized rocks responsible for field anomalies belong to the surface layer of the Earth or earth's crust.
Remanence can only occur for temperatures below the Curie point. For an average temperature increase of 20.degree. C. per km, said temperature is reached before the first 100 km.
For the non-geologist, the rocks of the earth's crust are therefore magnetized elements, whose magnetization has a random direction and intensity. The magnetism of rocks is dealt with in the JACOBS 89 document.
The behaviour of the geomagnetic field will be considered hereinafter. The origin of the geomagnetic field is outside the Earth. It is due to solar activity and to movements of charged particles generated by the sun around the Earth. One of its properties is its space coherence.
The physical analysis of phenomena involved shows that geomagnetic pulsations can be predicted with the aid of linear filters F.sub.u and F.sub.v, cf. the BERDICHEVSKI 84 document. These linear filters F.sub.u and F.sub.v are variable in space, as can be seen in FIG. 1, which shows a plan view of the area 2 to be mapped (measurement of the magnetic field b) at sea (reference 4) and which also shows land references (the land carrying the reference 6).
It is also possible to see two directional magnetometers 8 in directions u and v.
An optimum prediction filter is constituted by filters Fu and Fv applicable to the signals of said directional magnetometers and dependent on the coordinates of the measurement point, but independent of time.
FIG. 1 shows a space prediction performed with the aid of two independent measurements (two components of the field) performed on land, whereas the prediction point is at sea. An optimum filter has at the most two dimensions.
As input channels it must have two independent field components for supplying an estimate on the geomagnetic noise measured at sea. The land measurement must be of a vectorial nature and have an accuracy at least equal to that of the measurements performed on the area to be mapped. The measurement can also be scalar and the filter obtained is then only of an optimum nature in certain special cases.
In conclusion, the magnetic anomalies on areas of a few hundred km.sup.2, due to the geology and local magnetic sources, constitute a space variable field superimposed on the Gaussian field, whose measurement is made noisy by the geomagnetic pulsations.
The magnetic anomalies are produced by the magnetized rocks of the earth's crust and the upper mantle thereof.
Geological events, such as reliefs or contours, are added to the magnetic properties of the rocks in order to contribute to the local anomalies of the geological field.
A description will be given hereinafter of known processes for producing and extending a magnetic map.
The measurement of the geological field of which it is desired to obtain the map is accompanied by the recording of the geomagnetic noise and the noise of the measurement system. Therefore the production of highly accurate magnetic maps must obtain freedom from such noise and in particular the geomagnetic noise.
The simplest method consists of not carrying out filtering and of using noisy measurements of the earth's field directly prior to interpolation. This leads to measurements of the geological field, whose error is of the same order of magnitude as the geomagnetic noise during the measurement (generally 1 to 10 nT).
When a geomagnetic noise reference is available, it is possible to obtain filtering by subtraction of the signal of said reference from the measurement of the earth's field. This presupposes that the transfer functions between the noise references and the geomagnetic noise on the area are unitary.
If the area to be mapped is remote from the references, the difference can have a significant geomagnetic noise residue. The signal to noise ratio of the maps produced in this way is low.
The present invention makes it possible to obviate the need for land references and to obtain maps which are virtually free from geomagnetic noise.
A high performance 2D (i.e. two-dimensional) filtering method for the measurements is given in the CARESS 89 document.
The earth's field data are passed into a 2D filter defined in the spectral range and constant over the entire mapped area. It is therefore necessary to have an anomaly field, whose properties are stationary over said area.
This approach makes it possible to carry out a 2D filtering of the measurements, take account of non-isotropic properties of the field lines and respect Laplace's equation of the potential fields. However, filtering is not of an optimum nature in areas where the field is not stationary in space .
The process according to the invention makes it possible to carry out an adaptive filtering according to the location of the measurement and take account of the non-stationary nature of the properties of the geological field, whilst also respecting Laplace's equation.
With regards to the analytical extension of a field, the tool for extending field maps has its origin in the analytical extension of complex functions (cf. the ZDHANOV 84 document). On the basis of these mathematical foundations, Zdhanov demonstrates all the theorems useful to the geophysicist for the manipulation of the fields.
The potential field extension relations are also e.g. demonstrated in the GRANT 65 document. These relations clearly show the upward extension effects (i.e. in the direction opposite to the sources), which attenuates the highest space frequencies.
This extension is used for smoothing the appearance of the magnetic maps, because it eliminates local shapes, which are of no use in the overall or regional understanding of an area.
The downward extension relation simply reveals the stability problems of the extension of a field in the direction of the sources giving rise to it. The extension downwards amplifies the shortest wavelengths by a factor proportional to exp(.vertline.k.vertline.Dz), in which k is the space frequency of the geological field and Dz the extension distance.
The upward and downward extension relations exist and are mathematically established for exact and continuous data. The downward extension is a problem where small input data errors can give rise to significant errors with respect to the estimates.
The experimental measurement data of the geological field available are subject to errors and are in finite number. It is therefore necessary to use regularizing methods in order to ensure a good validity of the downward extensions.
The above paragraphs demonstrate the difficulty of the downward extension operation. The putting into practice of the extension consequently requires particular care, when there are real, i.e. inaccurate, noisy and non-continuous measurements.
A practical validity study was carried out by Miller (cf. the MILLER 77 document) by comparing readings taken on the surface with direct measurements performed on the ocean bed and extended upwards. The results of his study are based on a frequency study of the measured surface profiles and those of the measured bed and which have been extended upwards and demonstrate that for short wavelengths, the surface readings are not coherent with those of the bed. Therefore the surface and bed informations are not of the same origin for these wavelengths.
Under the measurement conditions concerning the studied information, Miller shows that the readings taken on the bed are only slightly contaminated by noise (positioning error, parasitic movements of the measurement "fish", magnetism of the towing boat, geomagnetic noise) and can consequently be used here as a reference.
Thus, the validity of extended profiles is crucially dependent on this preliminary treatment or processing, whose parameters are difficult to estimate. The earth field data must be filtered in an optimum manner prior to extension.
The proposed pre-extension filtering is generally a contrivance which is not linked with the real physical properties of the anomaly field and which is intended to make it sufficiently smooth (i.e. attenuate the shortest wavelengths) in order to compensate the amplification of the term in exponential form referred to hereinbefore. This filter, recommended in the Grant 65 document, can eliminate the measurement noise, but can also deteriorate the signal of the geological field.
Finally, it is difficult to give a perfect cut-off frequency, i.e. regulate the regularization parameter of the extension and the results of the extensions obtained in this way cannot show the fine details.
This pre-filtering method is difficult to perform and not particularly well adapted to magnetic maps for variable beds for which the filtering would have to be adapted to the distance of the closest sources.
Caress and Parker disclose a method for the interpolation and extension of the field map of marine magnetic anomalies (cf. CARESS 89), pointing out that the aforementioned methods, whilst covering smooth interpolation methods, do not respect the marked anisotropy of the treated magnetic maps.
Their anomaly model is a stochastic procedure with stationary properties over the entire magnetic map characterized by a constant 2D spectrum. The constraints of an anomaly field also makes it necessary for them to obey the Laplace's equation and this is integrated in the model. The algorithm provided has the advantage of supplying the uncertainty associated with the interpolated value. The latter treatment method for the marine magnetic readings is of a high performance type for stationary property anomalies. The model is anisotropic and also respects the nature of the potential field.
However, the readings used for producing the prediction of the geological field cannot always constitute maps with stationary properties. In certain difficult and coastal areas (cf. the CHAVE 90 document), the ocean beds can vary between a few dozen and several thousand meters. The geological field cannot then be considered as stationary. The geomagnetic noise, with the present variations of several dozen nT, then constitutes a very serious disturbance.
In conclusion, the quality of the predictions of the determination of the geological field by optimum extension methods is crucially dependent on the quality of the starting map.
The present invention proposes a non-spatially stationary filtering process which respects Laplace's equation.
In addition, the use of the apparatus according to the invention leads to freedom from the geomagnetic noise and/or the anisotropy noise.
Consideration will now be given to the inverse geophysical problems. Geophysicists use inverse methods for the determination of certain parameters of the subsoil on the basis of measurements performed on the surface.
These inverse methods are used in gravimetry (cf. the RICHARD 84 document) and in geomagnetism (cf. e.g. the LE QUENTREC 91 document). The calculations performed aim at giving information on the subsoil.
The parameters of the subsoil found by inversion (cf. TARANTOLA 87) have the property of the "at best" generation of the measured data. Thus, inverse methods make it possible to find a physical subsoil model making it possible to re-create the measurements.
The geophysicist is interested in interpreting the parameters of the subsoil found by inversion. However, in potential field inversion problems the solution is not unique. The problem is fundamentally underdetermined. For continuous data without noise, it is impossible to find the real solution. Under these conditions, it is known to use filtered or unfiltered field measurements. From then is initially subtracted a regional field component not generated by the local geology.
The remaining anomaly data are due to local properties, which alone interest the geophysicist. These data are then inverted on a prior unknown magnetization distribution. The values of the parameters found make it possible to obtain information on the subsoil.
It is known that when two potential fields coincide on the same surface, they coincide everywhere (cf. the ZDHANOV 84 document).
This invention makes use of the said theorem for carrying out field extensions with the aid of the parameters of a subsoil model, determined by known inverse methods (cf. the TARANTOLA 87 document).
The present invention proposes rules for producing a model adapted to the extensions.